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Multi-level numerical methods that obtain the exact solution of a linear system are presented. The methods are devised by combining ideas from the full multi-grid algorithm and perfect reconstruction filters. The problem is stated as…
For improving image composition and aesthetic quality, most existing methods modulate the captured images by striking out redundant content near the image borders. However, such image cropping methods are limited in the range of image…
In the image inpainting task, the ability to repair both high-frequency and low-frequency information in the missing regions has a substantial influence on the quality of the restored image. However, existing inpainting methods usually fail…
A new algorithm is developed to jointly recover a temporal sequence of images from noisy and under-sampled Fourier data. Specifically, we consider the case where each data set is missing vital information that prevents its (individual)…
We present a multigrid iterative algorithm for solving a system of coupled free boundary problems for pricing American put options with regime-switching. The algorithm is based on our recently developed compact finite difference scheme…
We use Deep Operator Networks (DeepONets) to perform super-resolution reconstruction of the solutions of two types of partial differential equations and compare the model predictions with the results obtained using conventional…
Video frame extrapolation is a task to predict future frames when the past frames are given. Unlike previous studies that usually have been focused on the design of modules or construction of networks, we propose a novel…
The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an…
Traditional approaches to interpolate/extrapolate frames in a video sequence require accurate pixel correspondences between images, e.g., using optical flow. Their results stem on the accuracy of optical flow estimation, and could generate…
Existing artificial compression based reinitialization scheme for conservative level set method has a few drawbacks, like distortion of fluid-fluid interface, unphysical patch formation away from the interface and lack of mass conservation.…
Neural implicit functions have emerged as a powerful representation for surfaces in 3D. Such a function can encode a high quality surface with intricate details into the parameters of a deep neural network. However, optimizing for the…
The task of reconstructing smooth signals from streamed data in the form of signal samples arises in various applications. This work addresses such a task subject to a zero-delay response; that is, the smooth signal must be reconstructed…
We propose a compressive sensing algorithm that exploits geometric properties of images to recover images of high quality from few measurements. The image reconstruction is done by iterating the two following steps: 1) estimation of normal…
Deep learning techniques have made considerable progress in image inpainting, restoration, and reconstruction in the last few years. Image outpainting, also known as image extrapolation, lacks attention and practical approaches to be…
In this paper, a new class of \emph{Taylor-accelerated neural network interpolation operators} is introduced on quasi-uniform irregular grids. These operators improve existing neural network interpolation operators by incorporating Taylor…
We consider image denoising using a nonlinear diffusion process, where we solve unsteady partial differential equations with nonlinear coefficients. The noised image is given as an initial condition, and nonlinear coefficients are used to…
We present a new approach to the numerical upscaling for elliptic problems with rough diffusion coefficient at high contrast. It is based on the localizable orthogonal decomposition of $H^1$ into the image and the kernel of some novel…
Increasing the resolution of image sensors has been a never ending struggle since many years. In this paper, we propose a novel image sensor layout which allows for the acquisition of images at a higher resolution and improved quality. For…
In winter scenes, the degradation of images taken under snow can be pretty complex, where the spatial distribution of snowy degradation is varied from image to image. Recent methods adopt deep neural networks to directly recover clean…
Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial…